1. Results of Midterm 1 # of students 10 20 30 40 50 60 70 80 90 10010 20 30 40 50 60 70 80 90
100
points
Grade
Points A
> 85 B+
80-84 B
65-79 C+
60-64 C
45-59 D
< 45

2. Problem 1
(30) A system is comprised of 0.25 mole of an ideal monatomic gas at 00C and P=1 bar. When 3400 J of thermal energy are added to the system at constant pressure, the resultant expansion causes the system to perform 900 J of work. Calculate: (a) (3) the initial state (P,V,T), (b) (8) the final state (P,V,T), (c) (4) the change in internal energy for the process, U, and (d) (15) the change in entropy for the process, S.
(a)
The initial volume can be found from the ideal gas law:
(b)
The work is negative since the gas did work on the surroundings (the internal energy is lowered by this process).
The temperature in the final state:
(c)
To determine the change in internal energy, the first law is applied:
(d)
The change in entropy:

3. (25) One mole of an ideal diatomic gas goes through a quasi-static three-stage cycle (1-2, 2-3, 3-1) shown in the Figure. Process 3-1 is adiabatic; V1 and V2 are given.
Calculate the entropy change for each stage and for the whole cycle, Stotal (express all the results in terms of given V1 and V2). Did you get the expected result for Stotal? Explain.
Problem 2 P 1 2 3 V V1 V2
1-2
V = const
2 – 3
P = const  V  T
3 – 1
Q = 0 (quasistatic adiabatic = isentropic process)
as it should be for a quasi-static cyclic process
(quasi-static = reversible),
because S is a state function.

4. Problem 3
(20) Consider two systems of four ½-spins each, in a magnetic field. The spins in System 1 are completely aligned: N-N =4. The spins in System 2 are completely random, N = N. The two systems are brought together so that energy is exchanged between them. Energy conservation requires that the magnetic moment, and therefore the net spin, is unchanged, so that in equilibrium we have a system of eight spins with N-N =4.
What is the entropy of the combined system before and after they are brought into contact? Is this process permitted by the second law of thermodynamics?
System 1:
System 2:
Combined System:
Since Sfinal>Sinit, this process is permitted by the second law.

5. Problem 4
(25) A hot 0.5 kg metal at 800C is dropped into a large pool of water at 200C. The metal has a specific heat at constant pressure of 100 J/(kgK) independent of temperature.
(20) How much does the entropy of the metal change? How much does the total entropy (of both the metal and water) change? Does it increase or decrease?
(5) Calculate the ratio final/ initial, where final and initial are the multiplicities of the final equilibrium macropartition and the initial non-equilibrium macropartition, respectively.
(a)
(b)